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- Fibred_category abstract "Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs) of objects such as vector bundles can be defined. As an example, for each topological space there is the category of vector bundles on the space, and for every continuous map from a topological space X to another topological space Y is associated the pullback functor taking bundles on Y to bundles on X. Fibred categories formalise the system consisting of these categories and inverse image functors. Similar setups appear in various guises in mathematics, in particular in algebraic geometry, which is the context in which fibred categories originally appeared. Fibrations also play an important role in categorical semantics of type theory, and in particular that of dependent type theories.Fibred categories were introduced by Alexander Grothendieck in Grothendieck (1959), and developed in more detail by himself and Jean Giraud in Grothendieck (1971) in 1960/61, Giraud (1964) and Giraud (1971).".
- Fibred_category wikiPageExternalLink 0206203.
- Fibred_category wikiPageExternalLink 0412512.
- Fibred_category wikiPageExternalLink Grothendieck+fibration.
- Fibred_category wikiPageExternalLink 1183741771.
- Fibred_category wikiPageExternalLink bookinfo.html.
- Fibred_category wikiPageExternalLink index.html.
- Fibred_category wikiPageExternalLink FibLec.pdf.
- Fibred_category wikiPageExternalLink 22-08abs.html.
- Fibred_category wikiPageID "2086749".
- Fibred_category wikiPageLength "23720".
- Fibred_category wikiPageOutDegree "66".
- Fibred_category wikiPageRevisionID "694593056".
- Fibred_category wikiPageWikiLink 2-category.
- Fibred_category wikiPageWikiLink Alexander_Grothendieck.
- Fibred_category wikiPageWikiLink Algebra.
- Fibred_category wikiPageWikiLink Algebraic_geometry.
- Fibred_category wikiPageWikiLink Algebraic_variety.
- Fibred_category wikiPageWikiLink Axiom_of_choice.
- Fibred_category wikiPageWikiLink Category:Category_theory.
- Fibred_category wikiPageWikiLink Category_(mathematics).
- Fibred_category wikiPageWikiLink Cleavage_(mathematics).
- Fibred_category wikiPageWikiLink Coherent_sheaf.
- Fibred_category wikiPageWikiLink Comma_category.
- Fibred_category wikiPageWikiLink Continuous_function.
- Fibred_category wikiPageWikiLink Dependent_type.
- Fibred_category wikiPageWikiLink Descent_(mathematics).
- Fibred_category wikiPageWikiLink Direct_image_functor.
- Fibred_category wikiPageWikiLink Equivalence_of_categories.
- Fibred_category wikiPageWikiLink Fiber_bundle.
- Fibred_category wikiPageWikiLink Fibration.
- Fibred_category wikiPageWikiLink Full_and_faithful_functors.
- Fibred_category wikiPageWikiLink Functor.
- Fibred_category wikiPageWikiLink Geometry.
- Fibred_category wikiPageWikiLink Grothendieck_construction.
- Fibred_category wikiPageWikiLink Grothendieck_universe.
- Fibred_category wikiPageWikiLink Group_(mathematics).
- Fibred_category wikiPageWikiLink Group_extension.
- Fibred_category wikiPageWikiLink Group_theory.
- Fibred_category wikiPageWikiLink Groupoid.
- Fibred_category wikiPageWikiLink Homomorphism.
- Fibred_category wikiPageWikiLink Initial_and_terminal_objects.
- Fibred_category wikiPageWikiLink Isomorphism.
- Fibred_category wikiPageWikiLink Jean_Giraud_(mathematician).
- Fibred_category wikiPageWikiLink Map_(mathematics).
- Fibred_category wikiPageWikiLink Mathematics.
- Fibred_category wikiPageWikiLink Morphism.
- Fibred_category wikiPageWikiLink Natural_transformation.
- Fibred_category wikiPageWikiLink Principal_bundle.
- Fibred_category wikiPageWikiLink Pullback_(category_theory).
- Fibred_category wikiPageWikiLink Pullback_bundle.
- Fibred_category wikiPageWikiLink Ring_(mathematics).
- Fibred_category wikiPageWikiLink Scheme_(mathematics).
- Fibred_category wikiPageWikiLink Section_(category_theory).
- Fibred_category wikiPageWikiLink Set_theory.
- Fibred_category wikiPageWikiLink Sheaf_(mathematics).
- Fibred_category wikiPageWikiLink Springer_Science+Business_Media.
- Fibred_category wikiPageWikiLink Stack_(mathematics).
- Fibred_category wikiPageWikiLink Subcategory.
- Fibred_category wikiPageWikiLink Surjective_function.
- Fibred_category wikiPageWikiLink Thomas_Streicher.
- Fibred_category wikiPageWikiLink Topological_space.
- Fibred_category wikiPageWikiLink Topology.
- Fibred_category wikiPageWikiLink Topos.
- Fibred_category wikiPageWikiLink Type_theory.
- Fibred_category wikiPageWikiLink Vector_bundle.
- Fibred_category wikiPageWikiLink Vector_space.
- Fibred_category wikiPageWikiLinkText "Cartesian morphism".
- Fibred_category wikiPageWikiLinkText "Fibred categories".
- Fibred_category wikiPageWikiLinkText "Fibred category".
- Fibred_category wikiPageWikiLinkText "Fibred category#Cartesian morphisms and functors".
- Fibred_category wikiPageWikiLinkText "Fibred category#Co-cartesian morphisms and co-fibred categories".
- Fibred_category wikiPageWikiLinkText "categories fibred".
- Fibred_category wikiPageWikiLinkText "fibred categories".
- Fibred_category wikiPageWikiLinkText "fibred category".
- Fibred_category wikiPageWikiLinkText "fibred".
- Fibred_category wikiPageUsesTemplate Template:Cite_book.
- Fibred_category wikiPageUsesTemplate Template:Cite_conference.
- Fibred_category wikiPageUsesTemplate Template:Cite_journal.
- Fibred_category subject Category:Category_theory.
- Fibred_category hypernym Entities.
- Fibred_category type Organisation.
- Fibred_category type Function.
- Fibred_category comment "Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs) of objects such as vector bundles can be defined.".
- Fibred_category label "Fibred category".
- Fibred_category sameAs Q5446431.
- Fibred_category sameAs Νηματική_κατηγορία.
- Fibred_category sameAs 올범주.
- Fibred_category sameAs m.02y_58g.
- Fibred_category sameAs Q5446431.
- Fibred_category wasDerivedFrom Fibred_category?oldid=694593056.
- Fibred_category isPrimaryTopicOf Fibred_category.